The attack left three people dead and wounded 13 others, including five who are in a serious condition.

A police source told Reuters that the shooter was "neutralised".

French police patrol in the closed Christmas market (Christophe Ena/AP)

More than 700 officers were involved in the manhunt for 29-year-old Cherif Chekatt and prosecutors have opened a terror investigation into Tuesday's attack.

The police operation took place in the Strasbourg neighbourhood where Chekatt was last seen.

A French police official said security forces, including the elite Raid squad, took action based on a "supposition only" that Chekkat could be hiding in a nearby building.

The official said the operation was sparked by reports of a person moving through gardens in the area.

People pay respect and light candles the night following the shooting in Strasbourg (Christophe Ena/AP)

French interior minister Christophe Castaner, speaking at the Senate while the roughly two-hour operation was under way, said it was aimed at "removing doubts" but did not necessarily mean the suspect was in that area. He said several similar police operations have taken place since the attack.

Meanwhile, the Paris prosecutor's office said a fifth person had been arrested and placed in custody in connection with the investigation.

French gendarmes patrol in the streets of the city of Strasbourg, eastern France, following a shooting, Wednesday, Dec. 12, 2018. (AP Photo/Christophe Ena)

A spokesman said the man is a member of Chekatt's "entourage" but not a family member and he was placed in custody on Thursday morning. The four others detained were Chekatt's parents and two of his brothers.

Asked earlier about instructions given to police forces searching for Chekatt, government spokesman Benjamin Griveaux said the focus was on catching the suspect "as soon as possible," no matter whether he was dead or alive, and "put an end to the manhunt".

Police distributed a photo of Chekatt, who was wounded in an exchange of fire with security forces, with the warning: "Individual dangerous, above all do not intervene."

Chekatt allegedly shouted "God is great!" in Arabic and sprayed gunfire from a security zone near the Christmas market.

The government raised the terror alert level nationwide and deployed 1,800 additional soldiers across France to help patrol streets and secure crowded events.

Mr Griveaux also called on the "yellow vest" protesters not to take to the streets, as some members of the movement have planned a fifth round of demonstrations on Saturday across France to demand tax relief.

Strasbourg was in mourning, with candles lit and flowers left at the site of the attack. The Christmas market was closed at least again on Thursday.

On Wednesday evening, people prayed and sang in the nearby Protestant Church Saint-Pierre-le-Jeune.

Pastor Philippe Eber said this is a moment "to think of those who died in this city because of violence. We also are thinking about all of those who weep for them, the families".

Strasbourg resident Tassia Konstantinidis said "it's important to have a period of mourning and to remember the victims".

The dead included Thai tourist Anupong Suebsamarn, who was 45.

Italian Interior Minister Matteo Salvini said one Italian was among the wounded, in critical condition. The Europhonica radio consortium said Antonio Megalizzi, 28, was in Strasbourg to follow the session of the European Parliament when he was shot.

French authorities said that the suspect, born in Strasbourg, had run-ins with police from the age of 10 and his first conviction was at 13.

Chekatt had been convicted 27 times, mostly in France but also in Switzerland and Germany, for crimes including armed robbery. He had been flagged for extremism and was on a watch list.